Question

The dimensions of a modulus of elasticity are:
A.\[\left[ ML{{T}^{-2}} \right]\]
B.\[\left[ {{M}^{2}}{{L}^{-1}}{{T}^{-2}} \right]\]
C.\[\left[ M{{L}^{-1}}{{T}^{-2}} \right]\]
D.\[\left[ M{{L}^{-2}}{{T}^{^{-2}}} \right]\]

Answer 1

Hint: The proportion of the pressure applied to a body to the strain that outcomes in the body in light of it. The modulus of versatility of a material is a proportion of its firmness and for most materials stays steady over a scope of stress.

Complete answer:
Young modulus = \[\dfrac{stress}{strain}\]
= \[\dfrac{\dfrac{\dfrac{force}{area}}{\Delta L}}{L}\]
= \[\dfrac{\dfrac{\dfrac{ML{{T}^{-2}}}{{{M}^{0}}{{L}^{2}}{{T}^{0}}}}{{{M}^{0}}L{{T}^{0}}}}{{{M}^{0}}L{{T}^{0}}}\]
= \[[M{{L}^{-1}}{{T}^{-2}}]\].
The proportion of the longitudinal strain to the longitudinal pressure is called Young's modulus. The proportion of the weight on the body to the body's fragmentary decline in volume is the bulk modulus.
Young's modulus, otherwise called the versatile modulus, portrays the solidness of a material. It is the proportion of stress to strain, where stress is the applied power per unit territory, and strain is a proportion of the material's adjustment length because of the pressure.
Hard and weak materials like pottery have an exceptionally high youthful modulus since they can continue a great deal of worry before "yielding" (on account of fragile materials, breaking). Metals are more adaptable, so they start to yield at a lower pressure. Plastics will in general have exceptionally low moduli since they are regularly rather adaptable. Indeed, even fragile plastics have low moduli contrasted with metals since they are more fragile in general.

The correct answer is C.

Note:
Metals are held together by the covalent bonds. Polymers are held together by Van der Waals powers, which are basically frail. This is the reason the positioning of most noteworthy modulus to least is:
Earthenware production > metals > polymers